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"Center of mass" is a mass-weighted average position. "Centercould
of gravity" is a gravitational force-weighted average position (I
have said "weight-weighted"). If g is essentially constant over theThen we
system, the center of gravity is essentially at the center of mass.
can do without the term "center of gravity".
However, here's an example where both terms are useful.
Suppose a meter stick is in orbit about the earth. If the stick is NOT
horizontal, particles of the stick closer to the earth have a bit more
gravitational force than equal-mass particles farther from the earth.As a result,
the center of gravity is below the center of mass. Since we can treatfield.
the entire weight of the stick as acting at its center of gravity, the
weight of the stick exerts a torque about the stick's center of mass,
tending to align the stick's long axis with the earth's gravitational
This torque can be used to orient satellites (my memory isits
that the jargon is something like gravitational-gradient orientation).
Allowed to swing freely, the stick will oscillate back and forth about
alignment position. It's not hard to get a good approximation for
its period using centers of gravity--I did so many years back when the
AAPT was looking for experiments to be done in orbit.
Tom Sandin